17 20 20 triangle

Acute isosceles triangle.

Sides: a = 17   b = 20   c = 20

Area: T = 153.8832869417
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 50.30113268251° = 50°18'5″ = 0.87879237712 rad
Angle ∠ B = β = 64.84993365875° = 64°50'58″ = 1.13218344412 rad
Angle ∠ C = γ = 64.84993365875° = 64°50'58″ = 1.13218344412 rad

Height: ha = 18.10438669902
Height: hb = 15.38882869417
Height: hc = 15.38882869417

Median: ma = 18.10438669902
Median: mb = 15.63664957711
Median: mc = 15.63664957711

Inradius: r = 5.39993989269
Circumradius: R = 11.04773635333

Vertex coordinates: A[20; 0] B[0; 0] C[7.225; 15.38882869417]
Centroid: CG[9.075; 5.12994289806]
Coordinates of the circumscribed circle: U[10; 4.69551295017]
Coordinates of the inscribed circle: I[8.5; 5.39993989269]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.6998673175° = 129°41'55″ = 0.87879237712 rad
∠ B' = β' = 115.1510663413° = 115°9'2″ = 1.13218344412 rad
∠ C' = γ' = 115.1510663413° = 115°9'2″ = 1.13218344412 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 17 ; ; b = 20 ; ; c = 20 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 17+20+20 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-17)(28.5-20)(28.5-20) } ; ; T = sqrt{ 23679.94 } = 153.88 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 153.88 }{ 17 } = 18.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 153.88 }{ 20 } = 15.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 153.88 }{ 20 } = 15.39 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 17**2-20**2-20**2 }{ 2 * 20 * 20 } ) = 50° 18'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-17**2-20**2 }{ 2 * 17 * 20 } ) = 64° 50'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-17**2-20**2 }{ 2 * 20 * 17 } ) = 64° 50'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 153.88 }{ 28.5 } = 5.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 50° 18'5" } = 11.05 ; ;




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